"Let's do this step by step:"
\qquad \qquad f(x) = 10 sin ({πx}/6 - {2π}/3) +50 \qquad \quad =>
f'(x) = [ 10 sin ({πx}/6 - {2π}/3) ]' + [ 50 ]' \qquad \qquad \qquad \qquad \quad "by Sum Rule"
= 10 [ sin ({πx}/6 - {2π}/3) ]' + 0 \qquad \qquad \qquad \qquad "by Rules for Constants"
= 10 cos ({πx}/6 - {2π}/3) cdot ({πx}/6 - {2π}/3)' \qquad "Chain Rule with sin"
= 10 cos ({πx}/6 - {2π}/3) cdot ({π}/6 x- {2π}/3)' \qquad \qquad \qquad \quad \ "rewrite a little"
= 10 cos ({πx}/6 - {2π}/3) cdot [ ({π}/6) - 0].\qquad \qquad \ "Rules for Constants"
"Note that there are no more differentiations asked for now in"
"the last expression."
"This means we are at the beginning of the Simplification "
"Phase. No more derivatives now."
= 10({π}/6) cos ({πx}/6 - {2π}/3)
= {5π}/3 cos ({πx}/6 - {2π}/3).
"This is our answer."
"Summarizing:"
\qquad \qquad f(x) = 10 sin ({πx}/6 - {2π}/3) +50 \qquad \quad =>
\qquad \qquad \qquad \qquad \qquad \qquad f'(x) = {5π}/3 cos ({πx}/6 - {2π}/3).
